Operation involving a quadratic form

Question

Let $A=(a_{ij})$ be an inversible $n\times n$ matrix and $x$ some $n\times 1$ vector, now consider the quadratic $$ Q=x^T A x $$ Now consider another $n\times n$ matrix $B=(b_{ij})$ (inversible). I would like to find some matrix operation to convert $Q$ into $$ U=x^T C x, $$ where $C=\left(\frac{a_{ij}}{b_{ij}}\right)$.